Related papers: Exact Solution to a Class of Generalized Kitaev Sp…
We present an exactly solvable spin-orbital model based on the Gamma-matrix generalization of a Kitaev-type Hamiltonian. In the presence of small magnetic fields, the model exhibits a critical phase with a spectrum characterized by…
This work develops a new method, based on the use of Gustafson's integrals and on the evaluation of singular integrals, allowing one to establish the unitarity of the separation of variables transform for infinite-dimensional…
We reconsider the quasi exactly solvable matrix models constructed recently by R. Zhdanov. The 2$\times$2 matrix operators representing the algebra sl(2) are generalized to matrices of arbitrary dimension and a similar construction is…
We lift the constraint of a diagonal representation of the Hamiltonian by searching for square integrable bases that support a tridiagonal matrix representation of the wave operator. Doing so results in exactly solvable problems with a…
We investigate a model containing two species of one-dimensional fermions interacting via a gauge field determined by the positions of all particles of the opposite species. The model can be solved exactly via a simple unitary…
Brief introduction to the discrete quantum mechanics is given together with the main results on various exactly solvable systems. Namely, the intertwining relations, shape invariance, Heisenberg operator solutions, annihilation/creation…
The exact quantum dynamics of a single spin-1/2 in a generic time-dependent classical magnetic field is investigated and compared with the quantum motion of a spin-1/2 studied by Rabi and Schwinger. The possibility of regarding the scenario…
In his seminal paper [1], Araki introduced an elegant extension of the Jordan-Wigner transformation which establishes a precise connection between quantum spin systems and Fermi lattice gases in one dimension in the so-called infinite…
The anisotropic XY-model in a transverse field (s=1/2) on the one-dimensional alternating superlattice (closed chain) is considered. The solution of the model is obtained by introducing a generalized Jordan-Wigner transformation which maps…
We study a set of exactly soluble spin models in one and two dimensions for any spin $S$. Its ground state, the excitation spectrum, quantum phase transition points, as well as dimensional crossover are determined.
We present here various techniques to work with clean and disordered quantum Ising chains, for the benefit of students and non-experts. Starting from the Jordan-Wigner transformation, which maps spin-1/2 systems into fermionic ones, we…
We systematically describe and classify 1-dimensional Schr\"odinger equations that can be solved in terms of hypergeometric type functions. Beside the well-known families, we explicitly describe 2 new classes of exactly solvable…
In the usual matrix-model approach to random discretized two-dimensional manifolds, one introduces n Ising spins on each cell, i.e. a discrete version of 2D quantum gravity coupled to matter with a central charge n/2. The matrix-model…
We provide explicit formulae for highest-weight to highest-weight correlation functions of perfect vertex operators of $U_q(\hat{\mathfrak{sl}(2)})$ at arbitrary integer level $\ell$. They are given in terms of certain Macdonald…
We consider gauged sigma-models from a Riemann surface into a Kaehler and hamiltonian G-manifold X. The supersymmetric N=2 theory can always be twisted to produce a gauged A-model. This model localizes to the moduli space of solutions of…
We solve exactly the general one-dimensional $O(N)$-invariant spin model taking values in the sphere $S^{N-1}$, with nearest-neighbor interactions, in finite volume with periodic boundary conditions, by an expansion in hyperspherical…
In this study, a spin-1/2 extended anisotropic XY chain has been introduced in which both time reversal and SU(2) symmetries are broken but $Z_2$ symmetry is preserved. Magnetic and topological phase diagrams in the parameter space have…
New exactly solvable quantum models are obtained with the help of the supersymmetric extencion of the nonstationary Schr/"odinger equation.
The unique off-shell fermionic gauge invariance of a vector-spinor field theory is found, and the invariant action is derived. The latter is Weyl invariant in any dimension in the massless limit, and it coincides with the singular point of…
Solvable vertex models in two dimensions are of importance in conformal field theory, phase transitions and integrable models. We consider here the $D_n$ spin vertex models, for $n$ which is odd. The models involve also the anti--spinor…